Partitioned Time Stepping Method for Fully Evolutionary Stokes-Darcy Flow with Beavers-Joseph Interface Conditions

In this report, a partitioned time stepping algorithm for transient flow in a porous medium coupled to a free flow in embedded conduits is analyzed. The coupled flow is modeled by the fully evolutionary Stokes-Darcy problem. This method requires only solve one, uncoupled Stokes and Darcy sub-physics and subdomain per time step. On the interface between the matrix and conduit, Beavers-Joseph interface conditions, instead of the simplified Beavers-Joseph-Saffman condition, are imposed. Under a modest time step restriction of the form 4t ≤ C where C = C(physical parameters) we prove stability of the method. We also derive error estimates. Numerical tests illustrate the validity of the theoretical results.